Information fusion has been one of the most successful theories developed for the past 20 years. However its meaning is still the subject of intense debate [2]. Despite its interpretational problems, researchers have recently started to successfully apply the apparatus of information synthesis to economy, finances, sensory fusion, databases integration etc. W.A. Sander in "Information Fusion"[6] describes the domain as follows:

Information Fusion or Data Fusion is the process of acquisition, filtering, correlation and integration of relevant information from various sources, like sensors, databases, knowledge bases and humans, into one representational format that is appropriate for deriving decisions regarding the interpretation of the information, system goals (like recognition, tracking or situation assessment), sensor management, or system control.

The aim of the tutorial is to give an overview of a few chosen models and information synthesis formalisms. We introduce three models of the fusion operator on theories/specifications. See e.g. [2] for other fusion models. No prior knowledge of information fusion is required, but we will assume participants have some basic knowledge of propositional and first-order logic.

Everyboy interested in logical modeling is welcome to join. The tutorial will be divided in the following three sessions.

I. Fusion by Products
We start with a quick historical overview of the fusion problem and we present the first fusion formalization under the generalized products of relational structures. Fraissé-Hintika-Galvin Autonomous Systems are the main tool for the decision synthesis of models of first-order theories under products of models ([4],[7],[8])

II. Los Ultrasynthesis
This lecture will be devoted to the exposition of the theory synthesis extracted from the analysis of the celebrated Los Ultraproduct Theorem ( [7],[8]). A special case of such an Ultrasynthesis Operator for theories of initial segments of a standard model of arithmetic [1], formulated by M.Mostowski, will be the principal subject of our investigations.

III. Sensory Minimization
We conclude by Dasarathy's [5] Sensory Fusion Minimization question on the minimal number of sensors necessary for the recognition of any object. Here the formalism of the sensory fusion is based on the multi-head finite automata recognition. Under the sensing multi-head automata model we prove the so-called '3-sensory Theorem' [3], according to which only three sensors are sufficient. .

Bibliography

[1] Michal Krynicki, Jerzy Tomasik, and Konrad Zdanowski. Theories of initial segments of standard models of arithmetics and their complete extensions Theoretical Computer Science, 412:3975–3991, 2011.

[2] M. Kokar, J. Tomasik, and J. Weyman. Formalizing classes of information fusion systems. Information Fusion: An International Journal on Multi-Sensor, Multi-Source Information, Vol.5:189–202, 2004.

[3] Jerzy Tomasik. Discrete dynamic approach to multisensory multitrack fusion. Proceedings of AeroSense'2000, volume Volume 4051, pages 369–379, Orlando, Florida, April 2000. NASA, IEEE.

[4] Jerzy Tomasik. Synthesis theories versus semantics integration for complex situation assessment. Proceeding of: NATO SET-169 8th Military Sensing Symposium, At Graf-Zeppelin-Haus in Friedrichshafen, Baden-Württemberg, GERMANY, volume SET-169 RSY-025. NATO, May 2011.

[5] Belur V. Dasarathy. Metric sensitivity of reciprocal relationship bonds in the knowledge discovery process. Proc. SPIE 4057, Data Mining and Knowledge Discovery: Theory, Tools, and Technology II, 2 (April 6, 2000); doi:10.1117/12.381719

[6] W. A. III. Sander. Information Fusion. In T. N. Dupuy, F. D. Margiotta, C. Johnson, J. Motley, and D. L. Bongard, editors, International Military and Defense Encyclopedia, Vol. 3, G-L, pp. 1259-1265.

[7] Chang, C. C. & Keisler, H. J. (1990). Model Theory Vol. 73. Elsevier

[8] Hodges, W. (1993). Model Theory (Encyclopedia of Mathematics and its Applications). Cambridge: Cambridge University Press.

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